Question

At what points do the graphs of y=2x+1 and y=-(x-1)^2+3 intersect?

A. (-3,5) and (1,3)
B. (-2,-6) and (2,2)
C. (-1,-1) and (1,3)
D. (1,3) and (3,7)

Answer 1

D. (1,3) and (3,7)

Explanation:

The graphs of y = 2x + 1 and y = -(x-1)^2 + 3 intersect at the points where they have the same y-coordinate. To find these points, we can set the two equations equal to each other and solve for x.

y = 2x + 1 = -(x-1)^2 + 3

2x + 1 = -x^2 + 2x + 2

x^2 - 4x + 1 = 0

(x-1)^2 = 0

x = 1

Now we can substitute this value of x into either of the given equations to find the corresponding y-coordinate.

y = 2x + 1 = 2(1) + 1 = 3

so the point of intersection is (1,3)

So the answer is D. (1,3) and (3,7)

Please note that the solution is valid only if the two equations y=2x+1 and y=-(x-1)^2+3 are defined for the same domain.